Writing on the envelope

A wealthy wise old woman feared that her daughter was lazy and as a result rather stupid.
When the old woman died, her will stipulated that her assets were to be liquidated and a check was to be written for the full amount.
The check was to be placed in one of three envelopes.
The other two envelopes would contain a blank piece of paper.
If the daughter could determine from the writing on the envelope which envelope contained the check, she would inherit her mother’s fortune, otherwise the fortune would go to the old woman’s favorite charity for animals.
The daughter was not allowed to touch the envelopes. Her decision had to be made based on the writing on the envelopes.
The daughter was told that only one envelope had a true statement and that the other two statements were false.
The envelopes had the following writing:

  1. This envelope does not have the check
  2. This envelope has the check
  3. The second envelope does not have the check

Which envelope should the daughter pick?

The daughter should pick envelope 1.
Statements 1 and 2 were false, and the only true statement was statement 3.
If the check was in envelope 1, that would make statement 1 false, statement 2 false and statement 3 is the only true statement.
If the check was in envelope 2, statements 1 and 2 would both be true.
If the check was in envelope 3, statements 1 and 3 would both be true.

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